I finally got my GarageBand working. Thanks for your hints!
I don't know why, but simply moving the ≈/Library/Fonts folder out of the home directory didn't work for me. I had to move them to another hard disk.
So, the sequence that worked for me, was:
1) Copy all the fonts from your home directory's Fonts folder to another disk.
2) Delete all the fonts in your home directory's Fonts folder.
3) Clear the caches: simply delete everything under ≈/Library/Caches - or use some handy helper app for this. I used Maintenance,
http://www.destinyofshadow.com/blog/
4) Restart. (In theory, logging out and back in should work too.)
As someone already suspected, the problem probably wasn't caused by some specific font, but just the sheer number of fonts. I had over 7000 installed. (Removing the broken fonts didn't work, either.)
I'm not even trying to understand why I had to move the fonts to an external disk to make the removal effective. Doesn't make sense to me. But anyways, that did the trick. Simply moving the Fonts folder to the desktop didn't.
I hope this helps.